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AIMS Mathematics

2016, Volume 1, Issue 3: 165-177. doi: 10.3934/Math.2016.3.165
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Research article

Applications of the Hille-Yosida theorem to the linearized equations of coupled sound and heat flow

  • Department of Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan
  • Received: 22 July 2016 Accepted: 03 August 2016 Published: 15 August 2016

  • This paper deals with the initial-value problem for the linearized equations of coupled sound and heat flow, in a bounded domain Ω in ${\mathbb{R}^N}$, with homogeneous Dirichlet boundary conditions. Existence and uniqueness of solutions to the problem are established by using the Hille-Yosida theorem. This paper gives a simpler proof than one by Carasso (1975). Moreover, regularity of solutions is established.

    Citation: Matsubara Ayaka, Yokota Tomomi. Applications of the Hille-Yosida theorem to the linearized equations of coupled sound and heat flow[J]. AIMS Mathematics, 2016, 1(3): 165-177. doi: 10.3934/Math.2016.3.165

    Related Papers:

  • This paper deals with the initial-value problem for the linearized equations of coupled sound and heat flow, in a bounded domain Ω in ${\mathbb{R}^N}$, with homogeneous Dirichlet boundary conditions. Existence and uniqueness of solutions to the problem are established by using the Hille-Yosida theorem. This paper gives a simpler proof than one by Carasso (1975). Moreover, regularity of solutions is established.


    加载中
    [1] H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Universitext. Springer, New York, 2011.
    [2] A. Carasso, Coupled sound and heat flow and the method of least squares, Math. Comp. 29 (1975), 447–463.
    [3] F. Harlow and A. Amsden, Fluid Dynamics, LASL Monograph LA 4700, Los Alamos Scientific Laboratories, Los Alamos, N. M., 1971.
    [4] R. D. Richtmyer and K.W. Morton, Difference Methods for Initial-Value Problems, Second edition, Interscience, New York, 1967.
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  • © 2016 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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